Atomic number is the number of protons in the nucleus; this number defines element identity.
Atomic weight (but not number) can vary within a single element. For example, Carbon-12 and Carbon-13 differ by an extra neutron in C-13. Both isotopes have the same chemistry, but C-13 is slightly heavier.
Atomic energetics and mass under a given temperature/pressure condition dictate in what state (solid, liquid, gas) an element exists at that temperature and pressure. For instance, Radon is a heavy atom (atomic weight 222), but exists as a gas at room temperature/pressure due to chemical inactivity. All other elements of similar atomic weight exist as solids at room conditions.
An element that changes to another element is caused by change in atomic number (proton count). Unstable atoms undergo radioactivity, which can result in conversion of a neutron to a proton, or vice versa. This causes a different amount of positive electrical charge. An electron is gained from or lost to the environment to rebalance atomic charges. The effect is a new element with a more stable atomic nucleus.
A detailed periodic table may contain element density (of the most common isotope), phase at room temperature and pressure, melting/boiling point, electronegativity and other properties. For atoms that are stable for tiny fractions of a second in minuscule amounts, atomic weight/number and electron configuration may be their only known properties.